J. Cole understands the hip-hop landscape has changed since his debut in 2011. Kendrick Lamar’s revelatory breakthrough set the bar for contemporary excellence, so Cole’s second release finds him with a chip on his shoulder as he attempts to up the ante. Claiming he’s “here for a greater purpose,” Cole has made a searching record with big ambitions. The MC, like Lamar, who appears on the A Tribe Called Quest-inspired “Forbidden Fruit,” has a conversational flow and a deeply personal approach. Cole continues to flash terrific storytelling technique with a rich gift for language and a deepened worldview. His concerns are antithetical to booty-clap rap as he weaves complex rhymes about race, the contradictions of fame, and cultural stereotypes. Sometimes he overreaches and gets intellectually sloppy (“Villuminati”) or stumbles on the obvious (“LAnd of the Snakes”). The insider hip-hop “Let Nas Down” is too insular to make its bigger points. The flawed set is buoyed by its clear vision and diverse musicality. (Out Tuesday)